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Investigation on the Cutting Force and Surface Quality in Harmonically Vibrated Broaching (HVB)
Investigation on the Cutting Force and Surface Quality in Harmonically Vibrated Broaching (HVB)
Mohammadian, Amirreza;Sadeqi Bajestani, Mahdi
Hindawi Advances in Tribology Volume 2023, Article ID 9917497, 11 pages https://doi.org/10.1155/2023/9917497 Research Article Investigation on the Cutting Force and Surface Quality in Harmonically Vibrated Broaching (HVB) 1 2 Amirreza Mohammadian and Mahdi Sadeqi Bajestani Mechanical Engineering Department, Sadjad University, Mashhad, Iran Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran Correspondence should be addressed to Mahdi Sadeqi Bajestani; email@example.com Received 1 February 2023; Revised 15 April 2023; Accepted 29 April 2023; Published 25 May 2023 Academic Editor: Lijesh Koottaparambil Copyright © 2023 Amirreza Mohammadian and Mahdi Sadeqi Bajestani. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper investigates the broaching process of phosphor-bronze (C54400) under diferent cutting conditions, and the infuential factors on cutting force and surface quality are studied. Te simulated cutting force implementing the force model based on the energy components also agrees with the results of experiments. In the frst part, diferent cutting velocities of V � 5, 10, 15, and 20 m/min are studied. In the second part, harmonic vibrations in the form of a sine wave with precise amplitude (A � 1 m/min) and frequencies (F � 55, 65, 85, and 95 Hz) are added in the direction of the cutting velocity. Te results revealed that an increase in the cutting velocity from 5 to 20 m/min results in a 40% enhancement in surface quality and a 20% decrease in the cutting force. Additionally, harmonic vibrations of higher frequencies can also contribute to a 35% higher surface quality and a 20% lower cutting force. Tis study will ultimately improve productivity in industries where broaching is considered the main manufacturing approach, such as automotive and aerospace, in which precision and accuracy are of paramount importance. difer depending on the section of the tool  (roughing, 1.Introduction fnishing, or calibration) and mechanical properties of the Broaching is one of the cutting processes, similar to sawing, workpiece material (Figure 1). which allows the production of diferent shapes on the One problem with the broaching process is tool wear, machined surface, e.g., fat, grooved, or even formed sur- which mostly afects edge fank surfaces (fank wear). faces. It is a single-path operation and is commonly carried However, it can also manifest as crater wear on the rake face. out as a postturning/postmilling process. Broaching is Multiple wear reasons can take place at once. However, economical, particularly in mass production, and can pro- abrasion is the most typical. A small degree of plastic de- duce surfaces with the desired roughness and high geo- formation can also be seen at the tips of the teeth. Addi- metrical accuracy . tionally, unexpected vibrations may cause edge chipping. Broaching is commonly used in high-tech industries Other processes that depend more on temperature are such as automotive and aerospace, where precision and uncommon since coolant oils regulate process accuracy are important . It is a process in which complex temperature . shapes can be produced with a high surface fnish, where the Forst  experimentally defned broaching and in- use of lubrication is common [3, 4]. Te broaching tool vestigated the efective causes and parameters of the process typically consists of three sections: roughing, fnishing, and in detail. Although it was published in 1932, it has never calibration. “Rise per tooth” is the parameter by which the been considered outdated. Terry and Cutright  in- material removal rate is decided. Other infuential geo- troduced a CAD (computer-aided design) process for metrical features include depth of cut (f ), rake angle (c), determining both the optimal values and operating con- clearance angle (α), and width of the land (b ), which may ditions for the broaching process. Kishawy et al.  fa 2 Advances in Tribology B b fa (a) (b) Figure 1: Geometrical features of the broaching tool . surveyed the mechanics of cutting and the efects of velocity on the cutting force and surface roughness in broaching tool teeth on the surface roughness of the Al7075-T6 broaching. Tey concluded that increasing cut- workpiece material through an energy-based analysis, and ting velocity will lead to lower cutting force and increased Teti et al.  reviewed the monitoring of machining surface quality. operation approaches and signal-processing strategies as In this paper, we propose the concept of harmonically well as their industrial applications. vibrated broaching (HVB) with diferent frequencies to Hosseini and Kishawy  presented a force model for reduce the cutting force and improve the surface roughness predicting cutting forces and chip load in orthogonal and of the process. We implemented the numerical force model using the energy balance and performed the experiment with oblique broaching processes by introducing the cutting edge as a parametric B-spline curve. Axinte et al.  phosphor-bronze (C54400) material to verify the results. studied the relationship between the quality of the ma- chined surface and the output signals of cutting force, 2. Force Model Using Energy Balance vibration, and acoustics sensors. Tey implemented surface roughness and optical and scanning electron microscopy to According to the model proposed by Kishawy et al. , the evaluate surface quality parameters such as profle de- cutting force can be quantifed as a function of power viation, chatter marks, and burr formation. Ozelkan et al. components as  studied a methodology to design a broaching tool, F � considering geometrical and physical limitations optimally. Complementary research was carried out by Ozturk and (1) Budak , where they studied a broaching tool optimi- P + P + P + P + P fF fR ch mn−ce pd zation method implementing cutting models and fnite � , element analysis (FEA) and abridged the outcome of the research into analytical forms that can be used in industrial where P (N.m/min) is the power consumed for the cutting applications. Axinte and Gindy  monitored the tool process, P and P are the power consumption at the tool- fF fR condition in diferent broaching conditions using the workpiece and tool-chip interface, respectively, P is the pd output signals extracted from some sensors in diferent tool consumed power for the plastic deformation of the work- conditions. Tey concluded that acoustic emission, vi- piece for material removal, P is the power used for the ch bration, and cutting force sensors are sensitive to broaching formation of the new surface, and P is the power mn-ce tool conditions. consumed due to the combined infuence of the minor Meng et al.  did thorough research on modelling and cutting edge, and V (m/min) is the cutting velocity. analysis of the broaching process enhanced by a forced vibration on cutting velocity created by a single harmonic 2.1. Tool Workpiece Interface. Te consumed power due to motion. Tey also considered three important notes: the cutting force of a single tooth, the number of teeth engaged, friction between the workpiece and the tool is calculated as and the infuence of simple harmonic motion. Ten, they  presented two single-tooth and two multiteeth models for P � F V, (2) fF fF broaching based on the empirical approach and shear angle theory. Finally, they verifed the results with where V (m/min) is the chip velocity and F is the friction fF experimental tests. force between the tool and workpiece, which can be cal- In a recent study, Orouji et al.  studied the infuence culated through. of cutting velocity on surface quality in the broaching ������ process on the workpiece material of Al-7075, resulting in Br (3) F � 0.625τ ρ l , fF y ce ac observations of enhanced surface quality and reduced cut- sin α nw ting force with the increase of cutting velocity. Later, Bajestani et al.  studied the efect of vibrations in cutting where Br is the Briks similarity criterion: Advances in Tribology 3 cos c 2.4. Plastic Deformation. Te layer being removed from the Br � , (4) workpiece consumes power calculated as  ξ − sin c n+1 1.5 1.5 and c (deg) is the normal rake angle, ξ is the chip com- V A Kln t − ln t C ω 2T 1T (11) p � , pd parison ratio, τ (N/m ) is the shear strength of the work- n + 1 piece material, ρ (m) is the radius of the cutting edge, α ce nw where K (N/m ) is the strength coefcient, n is the hardening (deg) is the normal fank angle, and l (m) is the engaged ac exponent of the workpiece material, and A (m ) is the uncut length of the edge in the cutting process. Te chip com- chip cross-sectional area. Substituting(6), (9), and (11) in (1) parison ratio, ξ, is calculated as results in a straightforward equation for measuring cutting 2T force per tooth in the broaching process ( (12)). ξ � , (5) �������������������� 1T 0.625τ ρ l V cos c y ce ac F � × where t (m) is the uncut chip thickness and t (m) is the C 1T 2T V sin α t − t sin c C nw 2T 1T formed chip thickness. (12) Substituting (3)–(5) in (2) results in n+1 1.5 1.5 �������������������� A Kln t − ln t 0.7 0.3 2T 1T cos c + 0.28σ t t b + . R 1T 1T 2T P � 0.625τ ρ l V . n + 1 (6) fF y ce ac sin α t − t sin c nw 2T 1T Te cutting force for a single tooth in the broaching process is calculated using (12). To determine the total cutting force, it has to be multiplied by the number of teeth 2.2. Tool-Chip Interface. Te power consumed at the tool- simultaneously engaged in the workpiece. chip interface originating from the friction between tool and In the simulations, broaching is assumed as a plain strain chip on the rake face P is calculated as fR process; therefore, the chip width before and after cutting is considered equal. Consequently, b would be the length of T1 P � τ l b , (7) fR c c 1T the cutting edge (l � b ), and the true uncut chip thickness, ac T1 t , is also considered to be equal to rise per tooth (t � f ). 1T 1T z where τ � 0.28 σ (N/m ) is the average shear stress at the Consequently, as illustrated in (5), where ξ is defned as c R tool-chip contact zone, σ (N/m ) is the ultimate tensile the ratio of the formed chip thickness and uncut chip strength of the workpiece material, b (m) is the chip thickness, dividing the measured thickness of the formed 1T width, and l (m) is tool-chip contact length and is cal- chip resulting from the experimental broaching process, culated as shown in Table 1, by the value of already known uncut chip thickness, the mean value of chip compression ratio is (8) l � t ξ , c 1T determined. Other required parameters to determine the cutting where k � 1.5 when ξ < 4 and k � 1.3 for ξ ≥ 4. In this re- force using (12) are related to the geometrical features of the search, experiments show that chip compression ratio is broaching tool and mechanical properties of the workpiece approximately 5, which will be discussed in the following material, which will be discussed in the following section. sections. Substituting (5) and (8) in (7), we will have 0.7 0.3 P � 0.28σ t t b V . (9) 3. Experimental Setup fR R 1T 2T 1T C Te experimental setup for verifying the force model using energy balance consists of the broaching tool, hydraulic 2.3. Formation of New Surfaces and the Efect of Minor Cutting cylinder, valves, accumulators, load cell, linear scale, and Edge. Te power consumed for the formation of new sur- fxture, which will be discussed in detail in the following faces is calculated as sections. Te overall specifcations of the servohydraulic system are tabulated in Table 2. P � E f , (10) ch fr cf In Figure 2, the position and arrangement of each where f is the frequency of chip formation and E is the component of the experimental setup and the direction of cf fr energy of fracture. P is negligible in the broaching process the broaching process are shown. ch due to the low cutting velocity and, consequently, the low Figure 3 also demonstrates the hydraulic circuit of the frequency of chip formation . Based on the numerical experimental setup. calculations considering the low cutting velocities employed Te tool implemented for this research is designed and in this study (5, 10, and 15 m/min), this parameter is in manufactured for these specifc setup confgurations and −5 a scale of 10 , which can be neglected compared to other research series. Te RENISHAW cyclone digitizer, with an power elements. Besides, as far as broaching does not have accuracy of 1 µm, is utilized to extract accurate geometrical a minor cutting edge, the parameter P is equal to features of the broaching tool. Te broaching tool specif- mn-ce zero . cations are mentioned in Table 3. 4 Advances in Tribology Table 1: Formed and uncut chip thickness for diferent cutting velocities. V t t ξ C 1T 2T 5 0.09 0.45 5.00 10 0.09 0.45 5.00 15 0.09 0.46 5.11 20 0.09 0.46 5.11 Table 2: Hydraulic system specifcations. Cylinder Working temperature 40–45 C Working pressure 150 bar Hydraulic Valve Maximum speed 30 m/min Maximum pressure 350 bar Working stroke 300 mm In Figure 4, the broaching tool, as well as its dimensional Load Cell characteristics extracted from the digitizer, can be seen. It consists of three main parts, the roughing teeth, where the rise per tooth is higher. Tey have the highest contribution to the material removal rate. Ten, there are the fnishing teeth, where the rise per tooth is lower, and they aim to improve the precision and surface roughness of the work- Broaching piece. Finally, the calibration teeth are responsible for en- Tool suring the intended material is removed as expected. Linear Besides, there is a thorough hole at the end of the tool Scale used for pulling the broaching tool through the guide in the broaching direction. Te workpiece material used for this study is phosphor- Workpiece bronze in the shape of blocks with dimensions of 30 × 40 × 40 mm. Te machined workpiece can be seen in Figure 5. Each block is used for two diferent tests for material- saving issues. Besides, Table 4 shows the mechanical Fixture properties of the workpiece material. Te fxture of the setup is made of Mo40 alloy steel and is designed and manufactured in our lab. Figure 2: Servohydraulic system components . Te relief valve is used for setting, decreasing, or maintaining outlet pressure constant in fuid transfer lines. Relief valves control the system pressure by bypassing the broached workpiece. Table 6 illustrates the detailed pressured fuid from a secondary line. Tese valves are specifcations of the sensors implemented in the research. designed to act at a particular preset pressure and protect the Te power unit includes an electric motor and pump, pressured equipment and tank from overload. In the current supplying oil with appropriate pressure and temperature for study, considering other system demands and the hardware the servohydraulic valve. To stabilize the oil pressure, two specifcations implemented for the research, the relief valve accumulators are also installed in the pressure and return preset pressure is set to 250 bars. lines of the hydraulic circuit. Te specifcations of the motor Besides the relief valve, the cylinder movement and and pump are listed in Table 7. speed are controlled by a servo solenoid hydraulic valve with PID controller is one of the most common controllers electrical position feedback. Te characteristics of hydraulic used in industry and academic research. In the design of any cylinders and valves are tabulated in Table 5. controller, the aim is to create a logical balance between Te digital linear scale reads the position data with 5 µm three characteristics: overshoot (M ), settling time (t ), and p s precision. In addition, to carry out cutting force tests, the delay time (t ). In PID controllers, this balance is reached Dacell CX101-T30 high-precision load cell measures the through the value of three parameters: proportional (K ), cutting force in each test. integral (K ), and derivative (K ). I D Before running the tests, the load cell was calibrated using Te Ziegler–Nichols  heuristic method is imple- diferent gauge blocks of already known weights. Taylor mented to acquire these parameters. At frst, K and K are I D Hobson Surtronic 25 proflometer with the accuracy of 1 μm considered to be zero. Ten, K is gradually increased until was implemented to measure the roughness parameter (R ) of the system reaches a steady oscillating state. Tis value is Broaching Direction Advances in Tribology 5 Pressure line Actuator accumulator Check valve Pressure line Pump accumulator Relief valve Servo valve Hydraulic power supply Figure 3: A simplifed model of the hydraulic circuit . Table 3: Specifcations of the broaching tool. In the second series of experiments, harmonic vibrations are applied to the cutting tool in the direction of the cutting Tool material 210Cr46 steel velocity in the form of a sine wave with a constant amplitude Type Pull end of A � 1 m/min and frequencies of F � 55, 65, 85, and 95 Hz. Tooth width 13 To obtain interpretable results for the relationship between Number of teeth 18 the cutting force, surface quality, and harmonic vibrations, Rise per tooth 0.09 mm Pitch 13.97 mm the cutting velocity during every single test has to be con- Edge radius 5 µm stant. To ensure this along the cutting stroke, the desired Rake angle 12.78 speed must be obtained quickly (in this research, during the Clearance angle 2.06 frst 0.01 seconds of the process) by applying the maximum Gullet radius 1.5 mm pressure of 200 bars. It has to be mentioned that higher Length of broach 200 mm frequencies were not chosen due to the limitations of the Cutting velocity 5–20 m/min experimental setup; however, the results with the chosen frequencies were already promising. Test results were then known as the ultimate coefcient (K ), and the period of this analyzed to investigate the infuence of cutting velocity and steady oscillation is (T ). Using K and T , K , K , and K are u u u P I D forced vibrations on the cutting force and surface quality. calculated. Having a rough yet educated estimation for PID parameters, experimental tests were carried out to narrow 5. Results and Discussion down these parameters to the optimum values presented in 5.1. Cutting Force and Cutting Velocity. Te average force in Table 8. Two PID controllers are required to provide op- erational freedom on the position and speed of the cylinder, the roughing section of the tool is considered the cutting force for each cutting velocity. Te cutting force-time graph the cutting velocity, and harmonic vibrations. Te frst PID controller is designed to control the valve for V � 10 m/min is plotted in Figure 8, which can verify the spool position and, accordingly, the position of the analytical model. broaching tool. To determine the optimum K’s for the “spool Te graph is divided into three segments. Tere are three PID” shown in Figure 6, ffteen diferent experiments were peaks in segment 1, each representing the engagement of a new tooth with the workpiece. Nevertheless, they are not conducted and carried out through which M , t , and t were p s d simultaneously minimized. As shown in Figure 7, the PID considered in force analysis since the process had reached the steady phase just after segment 1. In segment 2, there are block “Linear PID” is simulated in MATLAB 2019b and a SIMULINK circuit to enable speed control of the fve peaks, each of which stands for the initiation of en- gagement in the roughing section of the tool, preceded by broaching process. Te optimum results of the experiments are given in segment 3, which contains three peaks resulting from three fnishing teeth of the broaching tool. As the engagement of Table 8. Te second PID controller is designed to control the valve speed and enables us to add harmonic vibrations of the the tool workpiece initiates, the cutting force gradually increases until the maximum number of teeth is involved, desired characteristics to the cutting velocity. i.e., three teeth. Afterwards, the cutting force fuctuates in a specifc 4.Procedure range, reaching the end of the stroke, where the cutting force Empirical tests for this research can be divided into two magnitude drops to zero after the last tooth leaves the series. In the frst series of experiments, phosphor-bronze workpiece. Figure 8 also shows the agreement between the block is broached (without vibration) at diferent cutting experimental results and the simulated data. velocities of V � 5, 10, 15, and 20 m/min, then the cutting Te increase in cutting velocity has positive efects on the force and the workpiece surface roughness are measured and chip formation process and lowers the shearing coefcient of compared with the model. the workpiece, which consequently results in a lower cutting 77.17° 6 Advances in Tribology 13.97 R 1.50 12.78° DETAIL A TRUE R3.500 Calibration teeth Finishing teeth Roughing teeth Direction of Broaching Figure 4: Extracted information from the digitizer for broaching tool. Table 4: Mechanical properties of the workpiece material. Material Phosphor-bronze Young’s modulus (E) 110 GPa Yield strength (σ ) 531 MPa Ultimate strength (σ )  548 MPa Strength coefcient (K) 0.51 GPa Strain hardening exponent (n) 0.29 Chip compression ratio (ξ) 5 Shear strength (τ )  0.65 σ y R Average shear stress (τ ) 497 MPa respectively. Figure 9 shows the comparison of cutting force at diferent cutting velocities. Figure 10 shows the engagement and disengagement of the tool tooth with the workpiece. At the start of the en- gagement, three teeth are responsible for material removal, causing a peak in the force diagram, while with the disen- gagement of a tooth, the magnitude of the force falls dra- matically. Te rise and fall of the force are strongly Figure 5: Broached workpiece. dependent on “rise per tooth,” which is obviously higher in the roughing section, causing higher peaks in that area. force. A case in point is the increase in cutting velocity from Te increase in the cutting force for each engagement V � 5 to 20 m/min, where the average cutting force en- of a new tooth at diferent cutting velocities varies counters a decrease of at least 20% from 4600 to 3600 N, depending on the value of the cutting velocity with an 30 40 19.293 2.06° 0.56 0.09 17.974 1.38° Advances in Tribology 7 Table 5: Valves and cylinder specifcations. Table 7: Hydraulic power pack specifcations. Manufacturer Diplomatic Type 3-phase Technical code MCD6-SP/51 N/K Electric motor Nominal power 1.1 KW Pressure limit Up to 350 bar Nominal revolution 1395 rev/min Relief valve Max fow 75 L/min Type Gear pump Fluid temperature −20 to 80 C Volume 2.7 cm /rev Hydraulic pump Viscosity 25 cSt Nominal fow rate 3.7 L/min Technical code 4WRPH 6 C3B12L Max pressure 250 bar Nominal fow 12 L/min Voltage 24 V/min Servo valve Table 8: Optimum PID parameters. Actuator Servo solenoid Max working pressure 250 bar Parameter Position control Velocity control Max solenoid current 2.7 A t 0.727 0.217 Cylinder type Two-way M 0 0 Cylinder diameter 40 mm t 0.523 0.103 Hydraulic cylinder Piston diameter 25 mm K 0.2 5 Displacement 195 mm K 2 0 Max pressure 210 bar K 0.001 0.001 Table 6: Sensors specifcations. tool created kinetic energy improved the chip formation Precision 5 µm process and enhanced the material removal rate. Linear scale Max working speed 60 m/min Figure 11 shows the force-time graph for V � 10 m/min Supply 5 V and the harmonic vibrations of F � 95 Hz. Model UU It can explicitly show that the analytical model can be Capacity 1 ton verifed with the experimental procedure. Adding harmonic Load cell Output 2 mV/V vibrations, depending on the magnitude of the frequency, Working temperature −20 to 80 C lowers the cutting force by almost 20% at diferent cutting Accuracy 0.001 velocities. For instance, the average cutting force in the Display 8 inches roughing section at V � 10 m/min is 4236 N, whereas, in the Proflometer Filter Digital gauss presence of harmonic vibrations of 95 Hz, this value de- Parameters R creases to 3180 N. Figure 9 shows the comparison of the magnitude of the cutting force in diferent cutting conditions. inverse relationship. At the cutting velocity of V � 5 m/ Te increase in cutting velocity and frequency of har- min, per engagement of a new tooth in the roughing monic vibrations decrease the cutting force. By increasing section of the process, an increase of 1400 N in the cutting cutting velocity, the chip formation process is enhanced, and force was observed, where the amount was reduced to the shearing coefcient between the workpiece material and 1100 N and 500 N at cutting velocities of 10 and 20 m/min, the broaching tool tends to decrease, leading to a stable respectively. broaching process, and accordingly, the cutting force de- It can be seen that when the cutting velocity is 20 m/min, creases. Besides, an increase in the frequency of harmonic the increase in cutting force per new engagement is around vibrations has similar efects and causes a favorable decrease 700 N, while this amount is almost twice as much at 10 m/ in cutting force by creating intentional interruptions in the min, reaching F � 1300 N per engagement. broaching process. 5.2. Cutting Force and Harmonic Vibrations. Te next phase is to add intentional sine waves of predetermined amplitude 5.3. Surface Quality and Cutting Velocity. A comparison of and frequency to the cutting velocity to lower the cutting surface quality measurements in diferent cutting conditions force. Te sine wave has an amplitude of A � 1 m/min and is shown in Figure 12. In the frst phase of the research, frequencies of F � 55, 65, 85, and 95 Hz. which is conventional broaching, an increase in cutting Te general pattern of force diagrams is to some extent velocity from 5 to 20 m/min enhances the surface quality by up to 40%, reducing Ra from 3.2 to 1.8 μm. similar in both HVB and conventional broaching. Notwithstanding, the results of the experiments show the In the second phase, which is harmonically vibrated hammering efect of the tool teeth on the workpiece. Te broaching, the increase in vibration frequency from F � 0 to sinusoidal cutting movement considerably diferentiates the 95 Hz leads to a 35% reduction in surface roughness, re- broaching motion in the conventional process and HVB. Te ducing R from 3.2 to 2 μm in the cutting velocity of intermittent contact between the tool and the workpiece in V � 5 m/min. the direction of cutting velocity results in fuctuations in the In comparison to conventional broaching at 5 m/min, corresponding cutting force and consequently leads to adding a 95 Hz sine wave and increasing cutting velocity to a reduction in its magnitude. Harmonic vibrations of the 20 m/min enhances surface quality by up to 80%. 8 Advances in Tribology Valve Reference Input Analog 1 PID (z) + Output Saturation Spool PID Analog Output Analog Input Advantech Advantech Valve PCI-1711 PCI-1711 Response Analog Input Figure 6: SIMULINK circuit for position control. Valve Reference Repeating Analog PID (z) + PID (z) Sequence + Output Linear PID Spool PID Saturation Analog Output Advantech PCI-1711 Sin Wave Analog Input Digital Input Analog Input Repeating Valve Advantech Digital Input 1 Response Sequence PCI-1711 Advantech PCI-1711 Figure 7: Position and speed control . Segment 2. Roughing Segment 1. Segment 3. First three teeth that are not Finishing and considered in force analysis calibration 3000 due to their random behavior. 0 0.5 1 1.5 2 2.5 Time (s) Experimental Data Force Model Figure 8: Cutting force vs. time graph for V � 10 m/min in conventional broaching acquired experimentally versus based on the simulated data. Force (N) Advances in Tribology 9 510 15 20 Cutting Speed (m/min) f=0 f=85 Hz f=55 Hz f=95 Hz f=65 Hz Figure 9: Comparison of the cutting force under diferent cutting conditions. Engagement of the new tooth, causing Disengagement of the previous tooth, raise in force causing reduction in force Tooth No. 1 Tooth No. 3 Tooth No. 1 Tooth No. 3 Workpiece (a) (b) Figure 10: Engagement (a) and disengagement (b) of broaching tool teeth with the workpiece. Segment 2. Roughing section Segment 3. Mean force: 3180 N Finishing section Segment 1. 0 0.5 1 1.5 2 2.5 Time (s) Figure 11: Cutting force vs. time graph for V � 10 m/min in harmonically vibrated broaching F � 95 Hz. Force (N) Force (N) 10 Advances in Tribology 5 101520 Cutting Speed (m/min) f=0 f=85 Hz f=55 Hz f=95 Hz f=65 Hz Figure 12: Comparison of surface roughness under diferent cutting conditions. 6.Conclusion b : Chip width (m) 1T b : Tool land (mm) fa In this research, workpieces of phosphor-bronze material E : Energy of fracture fr were broached under diferent cutting conditions. F : Cutting force (N) (i) Te experiments are signifcantly in agreement with F : Te friction force between tool workpiece fF the force model based on the components of the F: Frequency (Hz) energy consumed in the broaching process. f: Cutting feed per revolution (m/rev) f : Depth of cut (m) (ii) Te increase in cutting velocity from V � 5 m/min f : Frequency of chip formation to 20 m/min causes a 40% reduction in surface cf K: Strength coefcient (N/m ) roughness. K , K , Derivative, integral and proportional coefcients D I (iii) In addition to surface roughness enhancement, K : higher cutting velocity leads to lower cutting force, K : Ultimate coefcient such that experiments revealed that the cutting l : Engaged length of cutting edge in the process (m) ac force at V � 20 m/min is almost 20% lower in l : Tool-chip contact length (m) comparison to V � 5 m/min. M : Overshoot (iv) HVB at a higher vibration frequency leads to an n: Hardening exponent of the workpiece material elevated surface quality of 20% when a sine wave of P : Power consumed for cutting (N.m/min) F � 95 Hz is intentionally added to the broaching P : Power (tool-chip interface) (N.m/min) fR process compared to conventional broaching. P : Power (tool-workpiece interface) (N.m/min) fF (v) Besides, HVB at F � 95 Hz, causes a 20% reduction P : Power consumed for plastic deformation (N.m/ pd in cutting force. min) P : Power for formation of new surface (N.m/min) (vi) Per engagement of a tooth of the broaching tool, the ch P : Power consumed due to minor cutting edge cutting force magnitude increases sharply up to mn-ce (N.m/min) a peak, then falls gradually until a new engagement R: Gullet radius (mm) has occurred. R : Mean roughness depth (µm) (vii) Based on the numerical approach and the experi- t : Uncut chip thickness (m) 1T ments, for cutting velocities higher than 10 m/min, t : Formed chip thickness (m) 2T it is assumed that the cutting force will decrease, t: Pitch (mm) and the surface roughness will increase. t : Delay time (s) t : Settling time (s) Nomenclature T : Steady oscillations period V : Cutting velocity (m/min) A: Amplitude (m/min) V: Chip velocity (m/min) A : Uncut chip cross-sectional area (m ) α: Clearance angle (deg) Br: Briks similarity criterion Ra (μ m) Advances in Tribology 11  E. Ozlu, ¨ A. Ebrahimi Araghizad, and E. Budak, “Broaching α : Tool orthogonal clearance (deg) tool design through force modelling and process simulation,” α : Normal fank angle (deg) nw CIRP Annals, vol. 69, no. 1, pp. 53–56, 2020. c: Rake angle (deg)  F. Klocke and A. 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Advances in Tribology
Hindawi Publishing Corporation
Investigation on the Cutting Force and Surface Quality in Harmonically Vibrated Broaching (HVB)
Sadeqi Bajestani, Mahdi
Advances in Tribology
, Volume 2023 –
May 25, 2023
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